arXiv subjects

Arunava Chakrabarti

Publications and source records attributed to Arunava Chakrabarti.

At least 55 records · Page 3Linked to original sources

arXiv2011

On the extendedness of eigenstates in a hierarchical lattice: a critical view

We take a critical view at the basic definition of extended single particle states in a non-translationally invariant system. For this, we present the case of a hierarchical lattice and incorporate long range interactions that are also distributed in a hierarchical fashion. We show that it is possible to explicitly construct eigenstates with constant amplitudes (normalized to unity) at every lattice point for special values of the electron- energy. However, the end-to-end transmission, corresponding to the above energy of the electron in such a hierarchical system depends strongly on a special correlation between the numerical values of the parameters of the Hamiltonian. Keeping the energy and the distribution of the amplitudes invariant, one can transform the lattice from conducting to insulating simply by tunning the numerical values of the long range interaction. The values of these interactions themselves display a fractal character.

cond-mat.mes-hall↗

arXiv2011

Strange eigenstates and anomalous transport in a Koch fractal with hierarchical interaction

Stationary states of non-interacting electrons on a Koch fractal are investigated within a tight binding approach. It is observed that if a hierarchically long range hopping is allowed, a suitable correlation between the parameters defining the Hamiltonian leads to spectacular changes in the transport properties of finite, but arbitrarily large fractals. Topologically identical structures, that are found to support the same distribution of the amplitudes of eigenstates, are conducting in some cases and insulating in the others, depending on the choice of the hierarchy parameter. The values of the hierarchical parameter themselves display a self-similar, fractal character.

cond-mat.dis-nn↗

arXiv2010

Magnetic Response of Interacting Electrons in a Fractal Network: A Mean Field Approach

The Hubbard model on a Sierpinski gasket fractal is carefully examined within a Hartree-Fock mean field approach. We examine the influence of a magnetic flux threading the gasket on its ground state energy, persistent current and the Drude weight. Both an isotropic gasket and its anisotropic counterpart have been examined. The variance in the patterns of the calculated physical quantities are discussed for two situations, viz, at half-filling and when the `band' is less than half-filled. The phase reversal of the persistent currents and the change of the Drude weight as a function of the Hubbard interaction are found to exhibit interesting patterns that have so far remained unaddressed.

cond-mat.mes-hall↗

arXiv2010

Electronic transport in an anisotropic Sierpinski gasket

We present exact results on certain electronic properties of an anisotropic Sierpinski gasket fractal. We use a tight binding Hamiltonian and work within the formalism of a real space renormalization group (RSRG) method. The anisotropy is introduced in the values of the nearest neighbor hopping integrals. An extensive numerical examination of the two terminal transmission spectrum and the flow of the hopping integrals under the RSRG iterations strongly suggest that an anisotropic gasket is more conducting than its isotropic counter part and that, even a minimal anisotropy in the hopping integrals generate {\it continuous bands} of eigenstates in the spectrum for finite Sierpinski gaskets of arbitrarily large size. We also discuss the effect of a magnetic field threading the planar gasket on its transport properties and calculate the persistent current in the system. The sensitivity of the persistent current on the anisotropy and on the band filling is also discussed.

cond-mat.mes-hall↗

arXiv2009

Controlled electron transport in coupled Aharonov-Bohm rings

We propose a simple model of two coupled mesoscopic rings threaded by magnetic flux which mimics a device for electron transmission in a controlled fashion. Within a tight binding formalism we work out exactly the conditions when a completely ballistic transmission can be triggered at any desired position of the Fermi level within a continuous range of energy. The switching action can be easily controlled by appropriately tuning the values of the flux through the two rings. The general transmission across the ring system displays interesting features characterized by the appearance and collapse of Fano resonances, and the suppression of the Aharonov-Bohm oscillations in several cases. We report and analyze exact analytical results for a few such cases.

cond-mat.other↗

arXiv2009

Electronic transmission in bent quantum wires

Electronic transmission in bent quantum wires modeled by the tight binding Hamiltonian, and clamped between ideal, semi-infinite leads is studied. The effect of `bending' the chain is simulated by introducing a non-zero hopping between the extremities of the wire. It is seen that the proximity of the two ends gives rise to Falo line shapes in the transmission spectrum. Transmission properties for both an ordered lattice and a Fibonacci quantum wire are discussed. In the quasi-periodic Fibonacci chain, the proximity of the two ends of the chain closes all the gaps in the spectrum and the spectrum loses it's Cantor set character.

cond-mat.mes-hall↗

arXiv2009

Flux induced semiconducting behavior of a quantum network

We show that a diamond shaped periodic network, recently proposed as a model of a spin filter (A. Aharony {\em et al.} \cite{aharon08}) is capable of behaving as a p-type or an n-type semiconductor depending on a suitable choice of the on-site potentials of the atoms occupying the vertices of the lattice, and the strength of the magnetic flux threading each plaquette of the network. A detailed study of the density of states of an infinite network is made together with the conductance of finite sized system to establish the idea.

cond-mat.mes-hall↗

arXiv2008

Ladder network as a mesoscopic switch: An exact result

We investigate the possibilities of a tight binding ladder network as a mesoscopic switching device. Several cases have been discussed in which any one or both the arms of the ladder can assume random, ordered or quasiperiodic distribution of atomic potentials. We show that, for a special choice of the Hamiltonian parameters it is possible to prove exactly the existence of mobility edges in such a system, which plays a central role in the switching action. We also present numerical results for the two-terminal conductance of a general model of a quasiperiodically grown ladder which support the general features of the electron states in such a network. The analysis might be helpful in fabricating mesoscopic or DNA switching devices.

cond-mat.mes-hall↗

arXiv2008

Metal-insulator transition in an aperiodic ladder network: an exact result

We show, in a completely analytical way, that a tight binding ladder network composed of atomic sites with on-site potentials distributed according to the quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple values of the Fermi energy. For specific values of the first and second neighbor electron hopping, the result is obtained exactly. With a more general model, we calculate the two-terminal conductance numerically. The numerical results corroborate the analytical findings and yield a richer variety of spectrum showing multiple mobility edges.

cond-mat.mes-hall↗

arXiv2007

Aharonov-Bohm ring with a side-coupled atomic cluster: magneto-transport and the selective switching effect

We report electronic transmission properties of a tight binding Aharonov-Bohm ring threaded by a magnetic flux, to one arm of which a finite cluster of atoms has been attached from one side. we demonstrate that, by suitably choosing the number of scatterers in each arm of the quantum ring and, by decoupling the ring from the atomic cluster, the transmission across the ring can be completely blocked when the flux threading the ring becomes equal to half the fundamental flux quantum. A transmission resonance then occurs immediately as the coupling between the ring and the impurity cluster is switched 'on'. It is shown that the delta-like transmission resonances occur precisely at the eigenvalues of the side coupled chain of atoms.Thw 'switching' effect can be observed either for all the eigenvalues of the isolated atomic cluster, or for a selected set of them, depending on the number of scatterers in the arms of the ring. The ring-dot coupling can be gradually increased to suppress the oscillations in the magneto-transmission completely. However, the suppression can lead either to a complete transparency or no transmission at all, occasionally accompanied by a reversal of phase at special values of the magnetic flux.

cond-mat.mes-hall↗

arXiv2006

Fano resonance in discrete lattice models: controlling lineshapes with impurities

The possibility of controlling Fano lineshapes in the electronic transmission is addressed in terms of a simple discrete model within a tight binding framework, in which a finite sized ordered chain is coupled from one side to an infinite linear chain (the `backbone') at one lattice point. It is found that, the profile of Fano resonance is strongly influenced by the presence of impurity atoms in the backbone. We specifically discuss the case with just two substitutional impurities sitting in the otherwise ordered backbone. Precise analytical formulae relating the locations of these impurities to the size of the side coupled chain have been presented. The nature of the transmission spectrum and the reversal of the pole-zero structures in the Fano resonance are discussed with the help of these formulae.

cond-mat.mes-hall↗

arXiv2006

Electronic transmission in a model quantum wire with side coupled quasiperiodic chains: Fano resonance and related issues

We present exact results for the transmission coefficient of a linear lattice at one or more sites of which we attach a Fibonacci quasiperiodic chain. Two cases have been discussed, viz, when a single quasiperiodic chain is coupled to a site of the host lattice and, when more than one dangling chains are grafted periodically along the backbone. Our interest is to observe the effect of increasing the size of the attached quasiperiodic chain on the transmission profile of the model wire. We find clear signature that, with a side coupled semi-infinite Fibonacci chain, the Cantor set structure of its energy spectrum should generate interesting multifractal character in the transmission spectrum of the host lattice. This gives us an opportunity to control the conductance of such systems and to devise novel switching mechanism that can act over arbitrarily small scales of energy. The Fano profiles in resonance are observed at various intervals of energy as well. Moreover, an increase in the number of such dangling chains may lead to the design of a kind of spin filters. This aspect is discussed.

cond-mat.mes-hall↗

arXiv2005

Extended electron states and magneto-transport in a 3-simplex fractal

We perform a real space renormalization group analysis to study the one electron eigenstates and the transmission coefficient across a 3-simplex fractal lattice of arbitrary size, in the presence of a magnetic field. In particular, we discuss the existence of extended electronic states and the influence of the magnetic field on the spectrum of the system. A general formulation is presented which enables us to deal with both the isotropic and the anisotropic cases. It is found that in general, the transmission across an anisotropic fractal is larger than its isotropic counterpart. Additionally, we point out an extremely interesting correlation between a subset of values of the external field, and the multiple fixed point cycles of the Hamiltonian corresponding to the extended eigenstates. A prescription for observing such correlations is proposed. This aspect may be important in the classification of the extended states in such deterministic structures.

cond-mat.dis-nn↗

arXiv2005

Electronic transport in a Cantor stub waveguide network

We investigate theoretically, the character of electronic eigenstates and transmission properties of a one dimensional array of stubs with Cantor geometry. Within the framework of real space re-normalization group (RSRG) and transfer matrix methods we analyze the resonant transmission and extended wave-functions in a Cantor array of stubs, which lack translational order. Apart from resonant states with high transmittance we unravel a whole family of wave-functions supported by such an array clamped between two-infinite ordered leads, which have an extended character in the RSRG scheme, but, for such states the transmission coefficient across the lead-sample-lead structure decays following a power-law as the system grows in size. This feature is explained from renormalization group ideas and may lead to the possibility of trapping of electronic, optical or acoustic waves in such hierarchical geometries.

cond-mat.dis-nn↗

arXiv2005

Unusual modes and photonic gaps in a Vicsek waveguide network

We propose a simple model of a waveguide network designed following the growth rule of a Vicsek fractal. We show, within the framework of real space renormalization group (RSRG) method, that such a design may lead to the appearance of unusual electromagnetic modes. Such modes exhibit an extended character in RSRG sense. However, they lead to a power law decay in the end-to-end transmission of light across such a network model as the size of the network increases. This, to our mind, may lead to an observation of power law localization of light in a fractal waveguide network. The general occurence of photonic band gaps and their change as a function of the parameters of the system are also discussed.

cond-mat.dis-nn↗

arXiv2004

Wave propagation in a quasi-periodic waveguide network

We investigate the transport properties of a classical wave propagating through a quasi-periodic Fibonacci array of waveguide segments in the form of loops. The formulation is general, and applicable for electromagnetic or acoustic waves through such structures. We examine the conditions for resonant transmission in a Fibonacci waveguide structure. The local positional correlation between the loops are found to be responsible for the resonance. We also show that, depending on the number of segments attached to a particular loop, the intensity at the nodes displays a perfectly periodic or a self-similar pattern. The former pattern corresponds to a perfectly extended mode of propagation, which is to be contrasted to the electron or phonon characteristics of a pure one dimensional Fibonacci quasi-crystal.

cond-mat.dis-nn↗

arXiv2003

Magneto-transport in periodic and quasiperiodic arrays of mesoscopic rings

We study theoretically the transmission properties of serially connected mesoscopic rings threaded by a magnetic flux. Within a tight-binding formalism we derive exact analytical results for the transmission through periodic and quasiperiodic Fibonacci arrays of rings of two different sizes. The role played by the number of scatterers in each arm of the ring is analyzed in some detail. The behavior of the transmission coefficient at a particular value of the energy of the incident electron is studied as a function of the magnetic flux (and vice versa) for both the periodic and quasiperiodic arrays of rings having different number of atoms in the arms. We find interesting resonance properties at specific values of the flux, as well as a power-law decay in the transmission coefficient as the number of rings increases, when the magnetic field is switched off. For the quasiperiodic Fibonacci sequence we discuss various features of the transmission characteristics as functions of energy and flux, including one special case where, at a special value of the energy and in the absence of any magnetic field, the transmittivity changes periodically as a function of the system size.

cond-mat.mes-hall↗

arXiv2001

Hidden dimers and the matrix maps: Fibonacci chains re-visited

The existence of cycles of the matrix maps in Fibonacci class of lattices is well established. We show that such cycles are intimately connected with the presence of interesting positional correlations among the constituent `atoms' in a one dimensional quasiperiodic lattice. We particularly address the transfer model of the classic golden mean Fibonacci chain where a six cycle of the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys. Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far been provided, to the best of our knowledge. In addition, we show that our prescription leads to a determination of other energy values for a mixed model of the Fibonacci chain, for which the full matrix map may have similar cyclic behaviour. Apart from the standard transfer-model of a golden mean Fibonacci chain, we address a variant of it and the silver mean lattice, where the existence of four cycles of the matrix map is already known to exist. The underlying positional correlations for all such cases are discussed in details.

cond-mat.dis-nn↗